Reply to 'Comment on "Ideal clocks -- a convenient fiction'' '

TL;DR

This paper rederives a de-excitation probability formula for a quantum scalar field in an accelerated cavity using Rindler modes, addressing prior concerns about mode usage and clarifying the calculation within the Rindler wedge.

Contribution

It provides a reformulation of the de-excitation formula entirely within the Rindler wedge, clarifying the role of Rindler modes in accelerated quantum field calculations.

Findings

Re-derivation of the de-excitation formula within the Rindler wedge

Clarification of the role of Rindler modes in the calculation

Addressing prior criticisms regarding mode usage

Abstract

For a quantum scalar field that is confined in a uniformly linearly accelerated cavity in Minkowski spacetime and interacts linearly with a scalar field that is not confined in the cavity, a de-excitation probability formula was obtained in [1] [K. Lorek et al, Class. Quant. Grav. 32, 175003 (2015) [arXiv:1503.01025]] by a first-order perturbation theory calculation. A recent Comment [2] [V. Toussaint, Class. Quant. Grav. 43, 068001 (2026)] questions this formula on the grounds that the calculation in [1] invokes Rindler modes both in the Rindler wedge of the accelerated cavity and in the opposing, causally disconnected Rindler wedge. In the present Reply we rederive the de-excitation formula given in [1] by a perturbation theory calculation that is formulated entirely within the Rindler wedge of the accelerated cavity. We also take the opportunity to comment on the role of the two sets of Rindler modes in the calculation presented in [1].